pub fn new_birthday_probability(n: u32) -> f64 {
    let mut nom = 1.;
    let mut denom = 1.;
    const N: u32 = 365;
    if n > N {
        1.0000
    } else {
        for i in 0..n {
            nom *= (N - i) as f64;
            denom *= N as f64;
        }
        1. - nom / denom
    }
}
